$lo{p}^2$

$($b$)$ By making the find operation more efficient

$($c$)$ By using a different data structure

$($d$)$ By using a different cost model

$37$ What is an example of an application where a queve is used?

$3.$ What are the three main types of analyses for glorithms?

$($a$)$ Best$-$case, worst$-$case, and average$-$case

$($a$)$ Managing a printer queue

$($b$)$ Implementing an undo function in a text editor

$($c$)$ Simulating a network of computers

$($b$)$ Empirical, theoretical, and practical

$($c$)$ Time complexity, space complexity, and correctness

$($d$)$ Divide$-$and$-$conquer, greedy, and dynamic programming

$32$ What does it mean for an algorithm to be optimal?

$($a$)$ It is the fastest algorithm for the problem

$($b$)$ It has the best possible worst$-$case running time

$($c$)$ It is the easiest algorithm to implement

$($d$)$ It uses the least amount of memory

$33$ What is the purpose of using tilde notation $()$ when analyzing algorithms?

$($a$)$ To represent the exact running time of an algorithm

$($b$)$ To simplify the analysis by ignoring lower$-$order terms

$($c$)$ To represent the best$-$case running time of an algorithm

$($d$)$ To represent the worst$-$case running time of an algorithm

$34$ What is the "doubling hypothesis" used for?

$($a$)$ To estimate the constant factor in the running time of an algorithm

$($b$)$ To estimate the exponent in the running time of an algorithm

$($c$)$ To compare the running times of two algorithms

$($d$)$ To determine the optimal algorithm for a problem

$35$ What are some system$-$dependent factors that can affect the running time of an algorithm?

$($a$)$ The input data and the algorithm itself

$($b$)$ The hardware, software, and operating system

$($c$)$ The programming language and the compiler

$($d$)$ The theoretical analysis and the empirical results $36$ What is an example of an application where a stack is used?